January 2020
Journal paper accepted
20/01/20/11:07 Filed in: Journal paper
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco, M. Ojeda-Aciego, B. De Baets. Relational Galois connections between transitive digraphs: characterization and construction. Information Sciences 519:439-450, 2020.
ABSTRACT This paper focuses on a twofold relational generalization of the notion of Galois connection. It is twofold because it is defined between sets endowed with arbitrary transitive relations and, moreover, both components of the connection are relations, not necessarily functions. A characterization theorem of the notion of relational Galois connection is provided and, then, it is proved that a suitable notion of closure can be obtained within this framework. Finally, we state a necessary and sufficient condition that allows to build a relational Galois connection starting from a single transitive digraph and a single binary relation.
ABSTRACT This paper focuses on a twofold relational generalization of the notion of Galois connection. It is twofold because it is defined between sets endowed with arbitrary transitive relations and, moreover, both components of the connection are relations, not necessarily functions. A characterization theorem of the notion of relational Galois connection is provided and, then, it is proved that a suitable notion of closure can be obtained within this framework. Finally, we state a necessary and sufficient condition that allows to build a relational Galois connection starting from a single transitive digraph and a single binary relation.
Conference papers accepted
15/01/20/08:51 Filed in: Conference papers
N. Madrid and M. Ojeda-Aciego. New measures of inclusion between fuzzy sets in terms of the f-index of inclusion. 24th Eur Conf on Artificial Intelligence (ECAI), Santiago de Compostela, 2020.
ABSTRACT The notion of inclusion is one of the most basic relations between sets, however, there is not a consensus about how to extend such a notion in fuzzy set theory. We introduce an alternative approach to previous methods in the literature in which we make use of the so-called f-index of inclusion. This approach has a main difference with respect to previous ones: instead of a value in [0,1], the measure of inclusion is identified with a function.
In this paper, using the f-index of inclusion we define two measures of inclusion in the standard sense, i.e., taking a value in [0,1] and then, we show that both measures are in accordance with the standard axiomatic approaches about measures of inclusion in the literature.
W. Conradie, D. Della Monica, E, Muñoz-Velasco and G. Sciavicco. An Approach to Fuzzy Modal Logic of Time Intervals. 24th Eur Conf on Artificial Intelligence (ECAI), Santiago de Compostela, 2020.
ABSTRACT Temporal reasoning based on intervals is nowadays ubiquitous in artificial intelligence, and the most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the eighties. There has been a great effort in the past in studying the expressive power and computational properties of the satisfiability problem for HS and its fragments, but only recently HS has been proposed as a suitable formalism for artificial intelligence applications. Such applications highlighted some of the intrinsic limits of HS: sometimes, when dealing with real-life data, many times one is not able to express temporal relations and propositional labels in a definite, crisp way. In this paper, following the seminal ideas of Fitting and Zadeh, among others, we present a fuzzy generalization of HS that partially solves such problems of expressive power, and we prove that, as in the crisp case, its satisfiability problem is generally undecidable.
ABSTRACT The notion of inclusion is one of the most basic relations between sets, however, there is not a consensus about how to extend such a notion in fuzzy set theory. We introduce an alternative approach to previous methods in the literature in which we make use of the so-called f-index of inclusion. This approach has a main difference with respect to previous ones: instead of a value in [0,1], the measure of inclusion is identified with a function.
In this paper, using the f-index of inclusion we define two measures of inclusion in the standard sense, i.e., taking a value in [0,1] and then, we show that both measures are in accordance with the standard axiomatic approaches about measures of inclusion in the literature.
W. Conradie, D. Della Monica, E, Muñoz-Velasco and G. Sciavicco. An Approach to Fuzzy Modal Logic of Time Intervals. 24th Eur Conf on Artificial Intelligence (ECAI), Santiago de Compostela, 2020.
ABSTRACT Temporal reasoning based on intervals is nowadays ubiquitous in artificial intelligence, and the most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the eighties. There has been a great effort in the past in studying the expressive power and computational properties of the satisfiability problem for HS and its fragments, but only recently HS has been proposed as a suitable formalism for artificial intelligence applications. Such applications highlighted some of the intrinsic limits of HS: sometimes, when dealing with real-life data, many times one is not able to express temporal relations and propositional labels in a definite, crisp way. In this paper, following the seminal ideas of Fitting and Zadeh, among others, we present a fuzzy generalization of HS that partially solves such problems of expressive power, and we prove that, as in the crisp case, its satisfiability problem is generally undecidable.